Abstract An operator associated with third-order potential derivatives and a force gradient operator corresponding to second-order potential derivatives are used together to design a number of new fourth-order explicit symplectic integrators for the natural splitting of a Hamiltonian into both the kinetic energy with a quadratic form of momenta and the potential energy as a function of position coordinates. Numerical simulations show that some new optimal symplectic algorithms are much better than their non-optimal counterparts in terms of accuracy of energy and position calculations.
Keywords celestial mechanics — methods: numerical
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